First, calculate the expected value of Assets ($A$) and Liabilities ($L$) at the end of the year:

• $E(A) = 500 \times (1 + 0.08) = 540$
• $E(L) = 410 \times (1 + 0.09) = 446.9$

Expected Surplus $E(S) = E(A) - E(L) = 540 - 446.9 = 93.1$

Next, calculate the standard deviations of Assets and Liabilities at the end of the year:

• $\sigma_A = 500 \times 0.15 = 75$
• $\sigma_L = 410 \times 0.08 = 32.8$

Calculate the variance of the surplus $S = A - L$: $\sigma_S^2 = \sigma_A^2 + \sigma_L^2 - 2 \times \rho \times \sigma_A \times \sigma_L$ $\sigma_S^2 = 75^2 + 32.8^2 - 2 \times 0.7 \times 75 \times 32.8$ $\sigma_S^2 = 5625 + 1075.84 - 3444 = 3256.84$ $\sigma_S = \sqrt{3256.84} \approx 57.0687$

To find the 95% confidence upper bound (95th percentile of the standard normal distribution corresponds to $Z = 1.645$): $S_{95\%} = E(S) + Z \times \sigma_S$ $S_{95\%} = 93.1 + 1.645 \times 57.0687$ $S_{95\%} = 93.1 + 93.878 \approx 186.978$ million.

This value rounds up to ₹187 million, which matches Option D.